Subtracting fractions with regrouping

To subtract fractions that require regrouping, there are four steps you must follow:

Rename with common denominators

Regroup the first fraction

Subtract the whole numbers and numerators

Simplify (if necessary)

The problem

$$2\frac{1}{3}\,-\,1\frac{1}{2}\,=$$

Rename with common denominators

$$2\frac{2}{6}\,-\,1\frac{3}{6}\,=$$

Regroup the first fraction

$$1\frac{8}{6}\,-\,1\frac{3}{6}\,=$$

Subtract

$$\frac{5}{6}$$

Simplify (if necessary)

not needed on this problem

Example 1: $3\frac{2}{5}\,-\,2\frac{4}{5}\,=$

Step 1: Model the first number

Step 2: Regroup the first number

Step 3: Subtract

Example 2: $4\frac{3}{7}\,-\,2\frac{5}{7}\,=$

Step 1: Model the first number

Step 2: Regroup the first number

Step 3: Subtract

So far, the examples shown have not involved fractions with different denominators. Before subtracting fractions with different denominators, you must first rename both fractions with a common denominator.

Example 3: $3\frac{1}{2}\,-\,1\frac{2}{3}\,=$

Step 1: Re-write the problem with common denominators

$3\frac{1}{2}\,-\,1\frac{2}{3}\,=$

$3\frac{3}{6}\,-\,1\frac{4}{6}\,=$

Step 2: Model the first number

Step 3: Regroup the first number

Step 4: Subtract

In summary, subtracting fractions that require regrouping is a 4-step process: